On the Uncertainty on the Phase of a Stable Linear System in the Periodic Disturbance Cancellation Problem

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This technical note shows the effectiveness of a fractional-order derivative controller with the addition of a proportional gain, to solve the problem of a sinusoidal disturbance cancellation for single-input, single-output, linear uncertain stable system. Uncertainties are specified in the form of bounds on the phase of the system at the disturbance frequency. Sufficient conditions are presented to guarantee the stability of the closed-loop system and consequently the disturbance rejection even if the uncertainty on the phase is greater than $\pi$ . For a class of systems whose frequency response entirely belongs to a generic half-plane passing through the origin of the complex plane, a regulator is designed without gain limitations.